The enigma of Vitruvian resonating vases and the relevance of the concept for today
Rob Godman
University of Hertfordshire, UK
<[email protected]>
1: Vitruvius – the person
Marco V. Pollio Vitruvius studied Greek philosophy and science around the 1st Century
BC. A practical exponent of his craft, he gained experience through his professional work
and was the architect of at least one complete unit of buildings for Augustus in the
reconstruction of Rome. As an indication of his diverse talents, he also oversaw
developments in the imperial artillery and military engines – making Vitruvius an important
figure in his day.
In modern times, Vitruvius has been regarded primarily as an architect but his explorations
of science and art in the widest sense shouldn't be forgotten. The emphasis of books I-V is
on architecture in the traditional sense of the word. The second five books contain
information relating to Greek science demonstrating the background Vitruvius had during
his studies and younger days. His research and experimentation is backed up by detailed
methodology (for instance, using a lighted lamp as an indicator for poisonous air in wells;
further tests for showing the danger of lead in fresh water pipes). Mathematical principles
and geometry assisted the delivery of his discoveries. The inspiration of science was at
one with art and literature (although this was not a philosophy specific to Vitruvius).
The science of the architect depends upon many disciplines and various apprenticeships
which are carried out in the art. (Vitruvius, on Architecture, Book I – on training of
architects, Loeb)
2: The Ten Books on Architecture
De Architechura is a collection of ten books detailing his practical experience with
traditional Greek theory of the time. Exact dates for the composition remain uncertain but it
is believed to have been written around 27 BC (towards the latter period of his life).
The complete treatise is detailed as follows:
Book 1: Architectural Principles
Book 2: Evolution of Building, Use of materials
Book 3: Ionic Temples
Book 4: Doric and Corinthian Temples
Book 5: Public Buildings, Theatres (and music), Baths and Harbours
Book 6: Town and Country Houses
Book 7: Interior Decoration
Book 8: Water Supply
Book 9: Dials and Clocks
Book 10: Mechanical and Military Engineering
There are a number of surviving manuscripts that have been used to create the current
published translations. These date from as early as the 8th Century (London, British
Museum). The text was rediscovered in the fifteenth century and has been studied by
renaissance architects to a wider range of student in the current day. A number of
translations of the text exist and are available in print. The two used for the purpose of this
paper are:
Vitruvius, The Ten Books on Architecture, translated by Morris Hicky Morgon, Dover
Vitruvius, on Architecture, Books I-V and Books VI-X, translated by Frank Granger, Loeb
The Loeb edition is particularly illuminating as it contains both the Latin and English
translation (needless to say, issues of translation are of paramount importance when
dealing with technical information from such an early source). The history of architectural
literature is taken by Vitruvius to begin with the theatre of Dionysus at Athens.
3: Theatre design
The design of a Roman theatre has much in common with its Greek counterpart. Before
discussing the differences it is perhaps worthwhile thinking a little about terminology. It is a
common mistake to name the semi-circular Greek and Roman theatres as amphitheatres.
They are not! An amphitheatre is circular (think about the Coliseum in Rome) and a theatre
is semi-circular (or at least close to it). The amphitheatre and theatre have vastly different
uses.
The theatre of the Greeks was built on the slope of a hill, securing sufficient elevation for
the back row from the naturally occurring landscape. The tiers were either cut directly into
rock or if the land was soft an excavation was made in the hillside and lined with rows of
benches. The steps were often faced with marble (as in the theatre of Dionysus at Athens).
The theatre of the Romans and hence Vitruvius, was potentially a freestanding structure
and therefore a much more complex design. The form of the Greek and Roman theatre
also differs in terms of proportion, as Vitruvius states:
The form of a [Roman] theatre is to be adjusted so, that from the centre of the dimension
allotted to the base of the perimeter a circle is to be described, in which are inscribed four
equilateral triangles, at equal distances from each other, whose points are to touch the
circumference of the circle. This is the method also practiced by astrologers in describing
the twelve celestial signs, according to the musical division of the constellations. Of these
triangles, the side of that which is nearest the scene will determine the face thereof in that
part where it cuts the circumference of the circle. Then through the centre a line is drawn
parallel to it, which will separate the pulpitum of the proscenium from the orchestra.
In the theatres of the Greeks the design is not made on the same principles as those
above mentioned. First, as to the general outline of the plan: whereas, in the Latin theatre,
the points of four triangles touch the circumference, in the theatres of the Greeks the
angles of three squares are substituted, and the side of that square which is nearest to the
place of the scene, at the points where it touches the circumference of the circle, is the
boundary of the proscenium. A line drawn parallel to this at the extremity of the circle, will
give the front of the scene. Through the centre of the orchestra, opposite to the
proscenium, another parallel line is drawn touching the circumference on the right and left,
with a radius equal to the distance from the left point, describe a circle on the right and
scene of the proscenium, and placing the foot of the compasses on the left hand point,
with the distance of the right hand interval, describe another circle on the left side of the
proscenium. (Vitruvius, The Ten Books on Architecture, Book V, Dover)
4: Greek/Roman Music
Before exploring the reasoning behind Vitruvius' concept of the resonating vases in
Roman theatres it is important to have an understanding behind music principles of the
time.
Harmony is an obscure and difficult musical science, but most difficult to those who are not
acquainted with the Greek language; because it is necessary to use many Greek words to
which there are none corresponding in Latin. I will therefore explain, to the best of my
ability, the doctrine of Aristoxenus, and annex his diagram, and will so designate the place
of each tone, that a person who studiously applies himself to the subject may very readily
understand it. (Vitruvius, The Ten Books on Architecture, Book V, Dover)
The systems as described by Aristoxenus and Pythagoras are somewhat different in terms
of technical information but particularly in terms of philosophy. Vitruvius (as can be seen
from above) follows the musical theory of Aristoxenus and it is this that the acoustic vases
are based upon. Whilst a detailed explanation of Greek and Roman musical theory is
outside the remit of this paper, some knowledge is required to understand Vitruvius'
thinking as regards the pitch of the vases.
Aristoxenus lived around the 4th Century BC and wrote a number of works on music and
related disciplines (Elements of Harmonics still survives). He sets out a theory of scale
structure and a method for analysis. At some considerable length he discusses the
required terminology. His definition of interval is somewhat different to that of the
Pythagoreans (which is based on ratio and proportion) in that he describes two pitches as
being bounded or marked off by two notes of different pitch (Landels). An important
definition is that of system. A system is a construction of intervals, the smallest group of
which is known as a tetrachord.
1/2
1
1
Diatonic
1/2
1/2
1 1/2
Chromatic
1/4
1/4
2
Enharmonic
FIGURE 1
The groups of four pitches in each tetrachord are always surrounded by the interval of a
fourth. Aristoxenus demonstrates three different types (diatonic, chromatic, enharmonic).
He uses the term hemitonion to describe our interval of a semitone and more complex
term of diesis for any interval smaller than a semitone (Landels). He does use
mathematical ratios to assist with the concept of microtones but also spoke of them in
terms of colour and other descriptive methods.
To make more complex pitch systems it is a simple matter of placing one tetrachord on top
of another (giving tetrachords based on cycles of fourths). This developed into the Greater
Complex System giving a two-octave construction and this is the method that Vitruvius
follows for the tuned vases.
5: Acoustic problems, vases, concept
Anyone who has visited a theatre (Greek or Roman) cannot fail to be impressed by the
overall clarity of sound without any kind of enhancement. A greater understanding of
acoustics can be identified as early as the beginning of the 5th century BC (Dionysos at
Athens and the theatre at Syracuse). The seats arranged in curved rows around the
circular orchestra formed large horizontal reflecting surfaces. This ensures that the path of
the sound waves travel from the source (the actor or singer) to each of the listeners in a
direct path (i.e. without reflection). Ironically, the shape of the theatres was not based on
scientific understanding but rather by accident. A site on the side of a hill, sloping down at
approximately 45 degrees gave a good acoustic result. Other portable solutions also
helped the acoustic. Backdrops helped high-frequency reflections (provided by painted
skins). It is believed the propagation of sound to the audience was aided by the
megaphone effect of the masks worn by the actors.
Further developments in the shape of theatres are all thought to have been due to
attempts at improving the acoustics. An increased length of the seating area (whilst
maintaining overall proportion) brought more of the audience close to the stage and thus
improved the acoustics, especially as less of the sound could escape at the sides of the
orchestra. However, the direction in which the actors were facing became of greater
importance, and the height of the stage building was increased and made of stone to
provide more reflection from behind and improve the distribution of the sound. A few
centuries later, and with the aid of his knowledge derived from Aristoxenus, Vitruvius was
attempting to solve other acoustical problems still prevalent in Roman theatres.
The Pythagoreans formulated the modern science of acoustics in Greece in the 6th
century BC. Aristoxenus examined the study of musical sounds further by going beyond
the source and propagation of sound to consider issues of perception. The work
concerning acoustics of Vitruvius is largely based on Aristoxenus's writings.
In theatres, also, are copper vases and these are placed in chambers under the rows of
seats in accordance with mathematical reckoning. The Greeks call them Echeia. The
differences of the sounds which arise are combined into musical symphonies or concords:
the circle of seats being divided into fourths and fifths and the octave. Hence, if the
delivery of the actor from the stage is adapted to these contrivances, when it reaches
them, it becomes fuller, and reaches the audience with a richer and sweeter note.
(Vitruvius, on Architecture, Book I, – on training of architects, Loeb)
Vitruvius' understanding of acoustics is extremely impressive for its time. He was aware of
an acoustical problem caused by the reflection of sound waves, namely that interference
to the original source is created by reflections making the original less clearly audible or
defined. Vitruvius called this reflection of sounds resonantia (which differs somewhat from
our modern day meaning of the word resonance which implies a sound being bounced
back and forth repeatedly at a specific pitch). Although such reflections were kept to a
minimum by the very design of Roman and Greek theatres, the resonantia would still have
been seen as a considerable problem. If any extraneous strong reflections come back to a
listener at slightly different times, then speech, for example, would have become difficult to
understand. As Vitruvius pointed out, an inflected language such as Latin is difficult to
understand when the final syllables of words arrive at slightly different times. These
theatres were outdoor venues often built into the side of a hill. The apparent dryness of the
resultant acoustic was also a problem for Vitruvius when dealing with music and he went
to considerable effort to invent a system that would counteract it. Resonating bronze vases
were his solution to this problem.
...let bronze vases be made, proportionate to the size of the theatre, and let them be so
fashioned that, when touched, they may produce with one another the notes of the fourth,
the fifth, and so on up to the double octave.
...the voice, uttered from the stage as from a centre, and spreading and striking against the
cavities of the different vases, as it comes in contact with them, will be increased in
clearness of sound, and will wake an harmonious note in unison with itself. (Vitruvius, The
Ten Books on Architecture, Book V, Dover)
Arguably, the combination of vases might be considered an early artificial reverberation
unit, with specific frequencies enhanced and others excluded. Obviously 'real'
reverberation does not function in such a way. How well might these vases have worked?
It remains unclear.
6: Vitruvius' use of musical theory within the theatre
Whilst there are no known original resonating vases in existence, a number of sites show
evidence of spaces (niches) where the vases would have been positioned.
12 pairs of compartments corresponding to those described by Vitruvius have been found
in the supporting wall of the uppermost row of seats of the Greek theatre at Aizani in
Phrygia, eight in the podium of the Roman theatre at Nicopolis, and seven in the Greek
theatre at Scythopolis in Syria. There are 20 niches in the upper part of the Greek theatre
of Gerasa in Jordan; at Ierapetra and Gortyn in Crete the theatres have 13 niches each;
and at Lyttos, also in Crete, there are three rows of 13 niches each. (Grove Dictionary
[Belli, 1854, Müller, 1886]).
Vitruvius states that different numbers of vases should be used depending on the size of
the theatre.
The method of marking out the positions in which the jars are to be placed is as follows. If
the theatre is not very large, a horizontal line should be marked out, halfway up the slope
[of the auditorium], and 13 vaulted cubicles built, with 12 equal intervals between them:
then the sounding jars as described above are placed in them.
So by this arrangement, the voice, radiating from the stage as from a centre, spreads itself
around [the auditorium]: and, by exciting resonance in particular vases, produces an
increased clarity and a series of notes which harmonize with itself. (Vitruvius, The Ten
Books on Architecture, Book V, Dover)
I
nëtë hyper bolaiön
II
nëtë die zeugmenon
III
paramese
IV
nëtë synhemmenön
V
mesë
VI
hypatë meson
in media
hypatë hypatön
Figure 2 shows the pitches (with Greek names) of the vases for a small theatre as
specified by Vitruvius. Vase I (nëtë hyper bolaiön) would be placed at either side of the
theatre with the in media vase (D 144) placed centrally. All others would be equidistant
between.
Larger theatres required a greater number of vases arranged in three horizontal rows (one
for the harmonia, a second for the chromatic and a third for the diatonic).
Vitruvius discusses why acoustic vases were not used in the theatres of Rome. Owing to
their wooden construction, singers who wished to increase the projection of their sound
could direct their voices towards the scene doors (valvae). When a theatre is made of solid
materials (such as stone) then it should be equipped with the vases as specified. Vitruvius
states that there are many examples in Greek cities (Corinth). The expense of the bronze
vases is also considered by Vitruvius:
many clever architects who have built theatres in small cities, from the want of others have
made use of earthen vases, yielding the proper tones, and have introduced them with
considerable advantage. (Vitruvius, The Ten Books on Architecture, Book V, Dover)
7: How did the vases sound?
It is likely that the function of the vases would have been to make some sounds louder
than others by allowing them to sympathetically vibrate when certain harmonics 'hit' them.
So, when a singer performs a perfectly in-tune scale, a number of vases would ring
creating a harmonic chord. An artificial reverberation (RT60 time estimated as 0·2–0·5
seconds, Landels) containing only those harmonics listed in the vases pitches would be
produced in an open-air theatre that would otherwise have none.
There may be another purpose for the vases other than those already mentioned. Some
believe the acoustic jars helped singers and those relying on ear for maintaining pitch to
keep to proper pitch. As indicated, the resonance of the vases would have given emphasis
to important pitches leaving the others silent. If the artificial reverberation concept is
difficult to accept, the assisted resonance idea is perhaps a little more attractive.
No definitive answer has been found to the question of authenticity and intent with regards
Vitruvian resonating vases. It is known that many of the original bronze vases were later
used for other purposes and even melted down. The earthenware vases are obviously
more prone to damage making them more unlikely to survive the ravages of time.
We have only limited information as to how large and what shape they were and this
information varies depending on which translation you use of the Vitruvian text. As a result,
a lot of reasoning and occasional down right guesswork is required in order to begin
piecing together the enigma of function and intent. However, a number of researchers
have produced a variety of reconstructions.
7.1 Virtual reconstructions - additive synthesis method
I began designing software based upon the concepts of Vitruvius in 1999. Max/MSP was
making real time synthesis on existing computers a practical possibility (a sixteen oscillator
additive synthesiser taking up around 30% of the CPU of an Apple Macintosh G3 266
computer). My experiments began by building a synthesizer using the ratios specified by
Vitruvius to see the types of sound I would generate. I made a number of assumptions as
to how I suspected the vases would have sounded (based upon the knowledge I had
gained as to the nature of the vases themselves and all other available documentation).
My principle assumption was that the harmonics should be largely sinusoidal.
I made no attempt at modelling the amplitude envelope of the vessel, as I was initially
interested in the pitch relationship of the harmonics (although a 'musical' fixed envelope
shape was used for each oscillator). This proved to be a very enlightening way to proceed
as it made me address issues of authenticity in the modelling process. Clearly this was an
artistic reconstruction based upon the Vitruvian principle where many of the physical
constraints (decay time and other naturally occurring acoustic phenomena could be largely
ignored as a result of being in the digital domain). My vases do not need to be 'touched' in
order to make them sound. They can simply be triggered by an algorithmic process, an
external triggering mechanism (sensor, video feed etc.) or rely on external sound being
analysed in order to trigger the appropriate oscillator. The code shown in FIGURE 4
(updated in February 2004) is largely derived from this initial idea.
Experiments were carried out using ten, sixteen and thirty-eight oscillators. These
numbers were based up the number of vases found in theatres depending on their size. In
the early experiments, one oscillator was used to represent one vessel. Clearly, a great
many more oscillators would be needed using the additive method if an accurate
representation was to be made as it is highly unlikely that a resonating vessel would
resonate with only one audible harmonic!
Figure 4 is an additive synthesis patch consisting of sixteen oscillators (ten shown here).
The programme can be used to trigger the oscillators via external sound (using percussive
or pitch detection objects, [bonk~] or [fiddle~] for example), which would be close to the
original function of the Vitruvian vases. Video input via SoftVNS, other sensor input or via
a quasi-random process for automatically 'sounding' the oscillators are also possible. As
we are in the digital domain, we are not dependant upon further physical constraints – my
Vitruvian vases do not have to decay once 'struck', nor are they dependant upon external
sound sources to resonate! Ironically, what began as an experiment (what would these
vases really have sounded like?), turned into something of an obsession. The assisted
resonance has featured in most of my work over the past four years, whether it is virtually
or physically through the use of musical instruments.
Touching the vases…
We can assume that the word 'touch' as used by Vitruvius means to make the vases ring
sympathetically when the vibration of a sound source with a particular frequency in its
harmonic series comes into contact. As has been stated, being in the digital domain frees
us from such physical constraints and we can experiment with how the vases may have
sounded in a variety of conditions. My first experiment was simply to see what they
sounded like being triggered without the need for an external sound source. Figure 5
shows such a patch with the triggering taking place via a pseudo random algorithm. This
created a continuously changing drone whereby all of the harmonics would sound at
different times.
Using a simple piece of C Code, random numbers are generated at timed intervals
specified by [metro] (on for each oscillator). If the number is below the value specified in
the [if] expression, a 0 is sent to the oscillators amplifier (turning it off). Otherwise the
number is sent through, multiplied by a number to bring it into a range between 0 and 1
and this in turn creates a sound.
Other methods for 'triggering' have included the use of David Rokeby's SoftVNS
extensions for Max/MSP. Video is captured via a camera and the software detects
movement as a series of vertical lines on the display. This movement is converted into a
number dependant on the ferocity of movement and this is multiplied by another number to
bring it into a range between 0 and 1, which in turn creates a sound in a similar way to
above. This type of interactive system is particularly effective in exploring the relationship
between movement and sound. The video camera and SoftVNS can easily be replaced by
other sensor soft/hardware. I have experimented with a variety of sensor types for use as
triggers (including touch, light, ultrasonic, infrared etc.)
Figure 6 shows a sub-patch used for video control (SoftVNS) of the Vitruvian drones. The
video image (not shown) is placed into the 'source' window and then the image is
subdivided into 16 vertical strands (under 'regions'). In turn, these strands are converted
into numbers that appear in [p region-send] (shown in FIGURE 6). This DarkVNS patch
was used for interactive control of other audio elements for the dark (http://
www.thedark.net - Braunarts, Culture-Online).
The numbers above the inlets are used to control the amplitude of the oscillators (the
integers are divided by 16384 to bring the new float into the range of 0 and 1).
Neither of these methods bares any resemblance to how the physical vases would have
functioned. To achieve this we have to understand what is happening to make the vases
resonate in the first place. The resonance is dependant upon external sound being
significantly strong enough to make the vessel vibrate. This is more complicated to model,
as it requires analysis of the sound source to determine its fundamental frequency (this is
because we only want specific vases to ring when they are 'hit' by these frequencies). As
has been stated, it is possible to achieve this with the [fiddle~] object and also combine
this with [bonk~] for detecting attacks. This is getting much closer, in terms of intention, to
what Vitruvius specified (from a sympathetic vibration point of view).
Envelope Shape and Spatialization
A single oscillator shown here can have its envelope shaped by a combination of the
[pack] and [line~] objects. It can clearly be seen from this example that the sound will fade
in over 2000ms and fade out again over 3000ms. The harmonics frequency is specified by
a number going into the left hand input of [* 1.]. All the other harmonics are based upon
ratios specified by Vitruvius to create the harmonics he has chosen. Although the
harmonics are accurate according to Vitruvius, clearly we are a long way from a true
reconstruction as the envelope shapes are far from reality.
[p sends] was used to send the output of the oscillators to the [mixer828]. This enabled the
oscillators to be sent to a multi-channel sound card. I have had the luxury of trying this
patch with a 16-speaker system although an octaphonic system is very effective. Vitruvius
is careful with the specifications of the localization of the vases. As can be seen from
chapter 6 of this paper, it would be a simple task to place a speaker in place of a vessel
within a real theatre. The spatialization of the vases is a little puzzling. Assuming that the
basic sound is sinusoidal, the actual positioning of the vases themselves shouldn't be
crucial owing to the relative lack of orientation of sinusoidal sounds from a psychoacoustic
stance. As usual, Vitruvius is very specific in his description of the layout. Presumably, he
simply felt that a semi-surround layout would be generally more effective in terms of
coverage. In terms of the digital reconstruction, there was little difference between the 8
and 16 speaker systems in terms of localisation. Indeed, quad and stereo are also very
effective in terms of the elusiveness of direction of source.
The patch above shows a relatively simplistic attempt at modelling a vessel with four
harmonics. If a RT60 reverberation time of 0.2 to 0.5 seconds is to be created then clearly
the envelope length needs to be of a similar order. In theory any number of harmonics
could be introduced but it is worthwhile remembering that the more oscillators being used
the greater the CPU load. For realities sake, a more detailed model rather than an
educated guess is required.
But, how important is reality when it comes down to interesting sound design and
composition? Issues that needed addressing were envelope shape and how to make this
dynamic dependant on how the vessel would be sympathetically struck; and, a more
accurate model of the vases actual resonance (it is likely the vases ring would have more
HF content initially and then be left with smaller amounts of LF – in a similar way to the
response of a bell). Additive synthesis is very inefficient at modelling sounds with large
numbers of harmonics so a new method needed to be found and integrated into the
programme.
At some stage I needed to make a decision as to my intentions behind this research reality and intent of purpose or artistic ideas derived from an ancient past. One thing was
sure; the sounds created using this system were very beautiful as they were and I have
continued to use them in my compositional output!
7.2 Virtual reconstructions - impulse response method
By clapping your hands in a church, you are listening to the church's response to the
impulse your palms have made. Commercially available convolution reverb software is
now available for anyone with a processor fast enough to run it. What this means is that it
is possible to 'sample' an acoustic and use it as a plug-in of your choice. Audioease have
developed Altiverb™ that allows the user the opportunity of combining a dry input sound
with an impulse response created in a real acoustic environment. They have provided
Impulse Response Pre-Processor software that allows the user to create their own impulse
responses.
By clapping your hands near a Vitruvian resonating vessel (if one was ever found or
reconstructed), you are listening to the vases response to the impulse your palms have
made. Perhaps this is getting closer to an accurate digital reconstruction and a means of
expanding into greater authenticity.
7.3 Physical reconstructions, building vases for analysis
Early in his career, Per Brüel attempted to duplicate the resonating vase concept by
physically building a series of vases to experiment with. None of Vitruvius' original
diagrams illustrating the size and shape of the bronze vases survive so Brüel's
experimental vases were made of clay in a wine-beaker shape. Brüel claims his
experiments showed that they enhanced reverberation at the resonant frequency
(although the vases were not tested in a real theatre).
Ideally, a complete set of vases needs to be made. However, the sheer cost of a minimum
of ten bronze vases has presumably prevented most researchers from pursuing the
project.
A combination of all available methods (physical and digital) may provide a truer picture
that is realizable commercially, scientifically and artistically.
8: A fusion of archaeology and composition?
With the aid of modern effects units that attempt to mimic real and imaginary spaces it may
be difficult to imagine the importance of the Vitruvian idea. Vitruvius may have invented the
whole notion of assisted resonance – an idea that is highly relevant today. Personally, I
have always found the idea of creating different acoustic spaces very appealing. Clearly,
my aims are very different from those of Vitruvius. I simply want to make an audience
question the visual/aural relationship that they experience.
Early Works
We found the Cross Bath (Figure 11) to be a fascinating space in terms of its location and
imagery. Most appealing was the fact that the floor and roof had no fixed boundaries (i.e.
the floor consisted of water with its source being a spring and the complete absence of a
roof!). This allowed sound in and out of the space. The recorded audio reflected this by
placing sound in juxtaposition and unison with the surroundings. Our aim was to capture
the space in as many ways as we saw fit. My continuing work with Jason Cornish has
been partly responsible for my fascination with Vitruvius.
Figure 12 was a somewhat tongue-in-cheek piece mimicking a teenager's obsession with
inexpensive cars and big sound systems! However, this sound system was triggered via a
series of sensors placed around the car that 'played' a variety of sampled car horns
(amongst other sounds…). The work was primarily about juxtaposing sound with false and
contradictory visual imagery. Despite the car clearly being stationary and the audience
moving around it, the sounds gave the impression of moving (using a distance-panner in
Max/MSP). The Vitruvian resonances were again present, giving an artificial 'glow' to the
rather austere and arguably modernist car park.
Similar sounds and contradictory imagery, this work (figure 13) explored the tunnel
acoustic with which we are all-familiar but also superimposed other 'false' acoustics on top
of it. I wanted to place sounds back into the tunnel that would have been present before its
conversion to a cycle tunnel. So, as the cyclists went through, they were chased by
mechanical engine sounds, spatialised in such a way (again, using my distance-panner in
Max/MSP) to give contradictory sensory experiences. Baring in mind that this was
projected through a stereo two-speaker system, it was remarkable how encompassing the
Vitruvian resonances were and how they worked with the other sounds already present.
Later Works
inside the eye of silence - a collaboration with Vivienne Spiteri
The following is a programme note by Vivienne Spiteri for inside the eye of silence. It
demonstrates our preoccupation with the Vitruvian concept and how we pushed the
principle away from a purely practical 'problem-solving' idea.
where does sound stop and silence begin, end,
sound, begin?
one of the harpsichord's best kept secrets lies hidden within her chambered spaces
between the notes, between those plucked strings (the sound of a harpsichord is like two
skeletons making love on a corrugated iron roof) whose piercing sting obliterates all
potential revelation of the secret : her resonance jiuces.
to isolate a single sound, to let the time-life of a solitary plucked string linger, live and rise
through to its natural end, is to reveal all : birth, breath, life, death and rebirth. all swell with
song. skeletons no more this full-bodied dancing sound, laughing and rejoicing, these rich
spectra liberated, escaped from their string prison, these wingéd frequencies, free as air.
air
ah, air
space
air-space and time
where do air, space and time unite?
"and time is te space your mind moves through" (gwendolyn macewen :
"vacuum genesis" from afterworlds 1987-88)
sound. sound becoming silence through air-travel, through open air, through air within a
space. an enclosed space? of time? time, ah time. sound's phantom vessel.
where does it wander? what is its voyage?
what is its voyage, never lowering anchor?
to step inside the eye of silence is to listen deeply, to feel it at your ear. for as long as air
and time give it wing, sound-in-silence-in-sound births and breathes itself, expanding,
contracting, like the lungs of a whale, huge and light as air.
enter vitruvius, ah vitruvius. he who knew the secret of the wingéd. his siren-song,
embodied in resonating bronze inside semi-circular spaces of another place, an other time,
drew forth, beguiled and captured the wild and wandering waves, colouring them lively :
live, alive, life. long life. longer still. unending
.
enter the spider, weaver of webs, silent siren temptress, vitruvius-collaborator inside the
eye, along her radii.
toronto. chemistry building. hanlan's point. harpsichord as siren temptress inside the eye,
weaving through space, resonanting her chambers.
listen, dive, fly, let the air wing you
around
space
is time
is sound is
silence
is
infnity's music
© Vivienne Spiteri August 2002
Commissioned by New Adventures in Sound Art for Sign-Waves, inside the eye of silence
was first shown in a multi-room environment using an octaphonic system at The Chemistry
Building, Toronto Island, Canada in August 2002. The concept behind the work was to
explore an imaginary resonance of the harpsichord. Rather than listening from a traditional
space, a few metres from the instrument, the aim was to give the impression of listening
and being able to navigate in almost microscopic detail, as if you were completely within
the instrument or even within the material it is made of. A number of 'real' and imaginary
resonances were explored and in common with many of my works from around this time,
the work made use of the Vitruvian resonances, giving the harpsichord source sounds a
space to exist in.
Ephemeral Cube/Solid - a collaboration with Colin Reid
Written shortly before inside the eye of silence, this work follows many of the basic ideas in
terms of space and how it is intended to be heard. Much of my previous work had explored
what happens to sound when it enters the atmosphere and reflects off different surfaces.
Ever been to the Taj Mahal in India? At the bottom of the building there's a chamber totally
enclosed in white marble, with one tiny entrance. The surfaces only reflect sound and
there is little opportunity for it to escape or to be absorbed.
Imagine; a room where carpets are imperceptibly laid down, rolled up again, the
thicknesses change; where the rooms surfaces change material, shape and design; where
the sound you hear is deep inside your head or coming from miles away in a cavern. The
sound source is no longer absorbed (with a decay) but it expands and evolves organically.
(Godman, Programme Note for 'installation' (Year of the Artist), Prema Arts Centre, Glos,
UK 2000.)
What might happen if we listen to these sounds under water? Or, what might happen if we
are inside a solid, moving through the molecules and listening to how they relate to each
other? Solid is an imaginary exploration of the resonance of a piece of glass, heard from
within, rather than outside in the air. (Godman, Programme Note for 'Solid' 2002)
Again, a number of acoustic spaces were designed and superimposed with each other.
Both inside the eye of silence and Solid are algorithmic works and use a series of
permutation tables to constantly change the order of how these spaces are presented.
This means the composition is likely to be noticeably different at different times of the day,
week, month etc. Solid was derived from the sound of glass. By using granular synthesis it
was possible to extend tiny fragments of sound and allow them to ride on the Vitruvian
resonances.
Figure 15 shows the Max/MSP patch used for operating Solid. The sub-patches [p pulsedchimes] through to [p drones] (shown in green) contain a number of pre-processed sound
files that are selected according to seven different permutation series. These series are
derived from English Change Ringing Patterns and are stored in the patch as [coll] objects.
The variables for these permutation series function as different sound files, no file (i.e.
producing silence) and the ability to alter the phase of the signal.
Resonance types used for Solid and inside the eye of silence
High grains (with distance-panner)
Convolutions
Comb reverberations
Middle grains (with distance-panner)
Low grains
Vitruvian resonances
(silence)
Nothing but drones…
It was always my intention to use the software to create sounds for installations. To my
surprise, they have proved remarkably popular for listening, simply for the sake of it! As
well as playback in gallery spaces they have been presented for radio broadcast.
Feedback from listeners is often varied, ranging from those that find the continuous sound
rather sinister to those that don't even notice they are there.
The Max/MSP code that I have written to create the drones is capable of different tunings
and numbers of oscillators. It has been suggested that these sounds could have
therapeutic properties. Whilst this is a long way from the original intensions of Vitruvius the
effect of these sounds on peoples emotions should not be ignored. There will be people
that find these sounds very relaxing and those that don't!
The intervals themselves are of course highly significant. Would these intervals have a
special meaning for the listeners or even spiritual or psychological importance in Greek
and Roman times? Music and science were an integral part of Greek (arguably less so for
Roman) life and played a role in most aspects of their day-to-day activities. If this was
more than a simple 'accompaniment' to these activities or the music (and hence the
intervallic relationship) had a more profound affect on them is difficult to ascertain. It would
be wrong for me to state that these digital reconstructions prove or disprove these
statements.
9: Conclusions
We should at some point be brave enough to ask (and potentially answer) a simple
question – did the vases as specified by Vitruvius actually do their intended job? There is
now a large amount of evidence to support the concept. Other resonating vases have
been found throughout history and some are still in use. There is no doubt that Vitruvius
was the source for vases used in medieval churches. In Europe there are examples found
in St. Clements, Sandwich, Kent, St. Peter Mancroft, Norwich, Fountains Abbey, York, UK
and St. Martin, Angers, Bjeresjoe, Sweden. Most of these jars are between 20 cm and 30
cm in length with fundamental frequencies of between 90 to 350 Hz (nor far away from the
pitches specified by Vitruvius). However, some of these examples of vases used in
churches may have been used to reduce reverberation and echoes by absorbing
resonance. Many were cemented into place and not placed loose as with the Vitruvian
examples. This would greatly reduce their efficiency as resonators. So, with these many
contradictions, it is hardly surprising that archaeologists are wary of the function of the
vases.
More research is required into modelling the vases from the information we have available.
As has been stated in this paper there are a number of options available. I suspect our
only real way of knowing how effective such a system would be, would be to physically
build some vases. Digital modelling using a variety of the techniques mentioned will give
us further clues as to the resultant effect. With visual reconstructions a practical possibility,
we should be able to build an accurate virtual reality of the Vitruvian space – a space that
has great relevance for archaeology, science and art.
10: Addendum
From conversations with Stephen Morris (Department of Physics, University of Toronto,
Canada) at the Subtle Technologies Conference, Toronto, May 2005, we believe that the
material of the vase itself is relatively unimportant. It is the air inside the vase that would
resonate and not the physical material of the vase (Vitruvius does state that bronze or
'earthenware' options would work and also suggests that the use of different material is
largely down to economic practicalities).
Ironically, the closest modern day vases to match the patterns suggested by
archaeologists and historians were found recently in a farm shop close to my home! The
Greek farmer is importing a variety of vases from Crete and selling them as garden
ornaments, water-features…
By spending some time singing into the vases, it soon became clear that these objects
resonated quite effectively at certain frequencies, and that these frequencies could be
changed by placing material (sand, water etc.) into the vase.
Analysis
A variety of techniques were used to investigate the acoustic properties of the vases. A
variety of impulse responses were created using the Altiverb™ Impulse Response PreProcessor software. The starter-pistol and sinusoidal sweep method were both used.
Sweeps gave the best results when a good quality loudspeaker was placed around 150cm
from the neck of the vase (not within it as the pictures indicate). The microphone used to
record the sweep was also placed in a variety of positions - the most dramatic result being
produced when placed several centimeters into the neck of the vase.
Figure Add.2 shows the waveform of a microphone recording of the impulse (sweep). This
file was saved as an impulse response inside Altiverb - the response being used as a VST
pluggin. A number of peaks can be seen. The frequencies of these peaks were analyzed
and then placed into an additive syntheziser (in Max/MSP).
The frequencies of these peaks for this vase are as follows (the vase can be 'transposed'
by changing its volume):
(hertz)
683
1070
1407
1790
2150
2465
2759
3130
3211
3518
3913
4539
4956
5035
5627
It is likely that there will be many higher harmonics, but these gave an accurate rendition of
the resonance of this vase. Interestingly, it is far from obvious what the fundamental of the
vase is! 683 Hz doesn't fit very nicely in terms of ratios found in the harmonic series with
those frequencies above it.
Figure Add.3 shows the simple synthesizer. It gave a clear way of manually testing the
pitch of the harmonics. These sounds were played into the vases using the loudspeakers
located in the neck (as indicated in Figure Add.1a-b).
The impulse responses within Altiverb gave interesting results when different sounds were
played through them. Speech gave strong resonant results (male voice). Some of my
existing synthesized drones were also played back. Obviously, those that contained a high
number of frequencies close to those listed above gave strong resonant results.
Figure Add.4 shows: Spectrogram, Sonogram, Oscilloscope
The graphs on the left (under Vessel) are an analysis for a 16 harmonic drone (with a
fundamental of B - 63Hz) being played through an impulse response of the earthenware
vase. Various peaks and troughs can be seen indicating that some frequencies are
reduced and some are increased in intensity. The graphs on the right are for comparison
(these are a direct send from the sound source).
Acknowledgements
I am very grateful to Stephen Morris (University of Toronto) and Lydia Sharman
(Concordia) for inspiring me to pursue the physical characteristics of these vases. It is my
aim in the near future to build a 'choir' of such vases and to physically reconstruct the
Echeia as specified by Vitruvius. This may give us some idea of the effectiveness of such
a system and, to an extent, reduce the number of unknowns still prevalent in this area of
research.
I would also like to thank Per Brüel for discussions in-person at the First Pan-American/
Iberian Meeting on Acoustics in Cancun, Mexico, 2002; Aaron Watson for equally
illuminating conversations at Reading University 2002 and private communication with
John Landels and Sam Moorhead (British Museum).
References
Grove, Dictionary of Music (various) 1998
Harrison, Kenneth. Vitruvius and Acoustic Jars in England during the Middle Ages, Ancient
Monuments Society 1967-68
James, J. The Music of the Spheres, Abacus, 1993
Landels, John G. Assisted Resonance in Ancient Theatres - Greece and Rome XIV,
Routledge 1967
Landels, John G. Music in Ancient Greece and Rome, Routledge 2000
Levin, F. R. The Manual of Harmonics of Nicomachus the Pythagorean (translation),
Phanes 1994
Roads, Curtis, The Computer Music Tutorial (for Granular Synthesis, 168-184), MIT 2001
Roads, Curtis, Microsound, MIT 2003
Robert G. Jahn, Paul Devereux, and Michael Ibison, Acoustic Resonances of Assorted
Ancient Structures J. Acoust. Soc. Am. 99(2): 649-658. February 1996)
Vitruvius, The Ten Books on Architecture, translated by Morris Hicky Morgon, Dover
Vitruvius, on Architecture, Books I-V and Books VI-X, translated by Frank Granger, Loeb
http://www.thedark.net (2004)
http://www.soundtravels.ca (2002)
http://www.digitaljourney.org.uk (2002)
http://www.philophony.com/pages (2001)
http://freespace.virgin.net/colin.reid2/ephemeralCube.htm (for further details on Ephemeral
Cube/Solid)
http://www.cycling74.com (for information regarding the Max/MSP programming language)
http://www.audioease.com (for information regarding Altiverb)
to cite this journal article:
Godman, R. (2006) The enigma of Vitruvian resonating vases and the relevance of the
concept for today. Working Papers in Art and Design 4
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